The present invention relates to a curve generator, in particular, relates to a curve generator for generating a plurality of smooth arcs in a graphic display device.
A prior graphic display device displays an approximate curve by generating a plurality of short linear lines or short vectors. However, said prior art has the disadvantages that the data or the short vectors required are very voluminous, thus the amount of memory for storing said data and the duration of time for displaying and/or transmitting the curve are very large. Further, the curve thus obtained by the approximation of a plurality of short vectors is not sufficiently smooth. To obtain a smoother curve, more data is required.
Other prior curve generators are, for instance, an analog integrator type curve generator (Timothy E. Johnson; "Analog Generator for Real-Time Display of Curves", Technical Report No-398, Lincoln Laboratory, MIT, 1965), and a digital curve generator with the combination of digital differential analyzers (James R. Armstrong; "Design of a Graphic Generator for Remote Terminal Application", IEEE Transactions for Computers, Vol. C-22, No. 5, 1973). However, those prior arts have the disadvantages that the structure or the circuit is very complicated and only a very limited curve can be generated by those curve generators, and thus those prior arts are not practicable.
Another prior art attempted to display a curve with a plurality of arcs. However, according to a prior arc type curve generator, a profile of a curve is defined uniquely by the coordinates of the whole given points and the tangential line at the start point, thus the curves thus generated have the undesired oscillatory phenomenon as shown in FIG. 1, in which the dotted line shows an ideal curve. That oscillatory phenomenon is discussed in detail in "An approximation of a curve with circular arcs", by T. Kamae and M. Kosugi, Information Processing Society of Japan, Vol 12, 1972. If an oscillatory phenomenon occurs, the generated curve oscillates as shown in FIG. 1, although it is smooth in a short section. Accordingly, a curve generator which generates a curve using a plurality of arcs has not been implemented in spite of the simple structure of same.
Other prior curve generators are U.S. Pat. No. 3,860,805, U.S. Pat. No. 3,325,630, and British Pat. No. 866,319. Those prior arts generate a curve between two points using a plurality of parabola or linear lines, and have the disadvantages that the structure of the curve generator is complicated and the curve thus generated is not sufficiently smooth.
Another prior art for generating a curve between two points is "Biarc Curves" by D. M. Bolton, (British Ship Research Association), Computer Aided Design, Vol 7, No. 2, 1975 (British publication). Although that document suggestes a curve generator which connects two points by a pair of arcs, that document does not refer to the locus of the junction point of the two arcs. Therefore, the flexibility of a curve thus generated is very limited, and further the calculation for obtaining a curve is rather complicated resulting a complicated device.